Question

A medical researcher wants to compare the pulse rates of smokers and non-smokers. He believes that the pulse rate for smokers and non-smokers is different and wants to test this claim at the 0.01 level of significance. A sample of 75 smokers has a mean pulse rate of 76, and a sample of 73 non-smokers has a mean pulse rate of 72. The population standard deviation of the pulse rates is known to be 9 for smokers and 10 for non-smokers. Let μ1 be the true mean pulse rate for smokers and μ2 be the true mean pulse rate for non-smokers.

Step 1. State the null and alternative hypotheses for the test.

Step 2. Compute the value of the test statistic. Round your answer to two decimal places.

Step 3. Find the p-value associated with the test statistic. Round your answer to four decimal places.

Step 4. Make the decision for the hypothesis test.

A) Reject Null Hypothesis

B) Fail to Reject Null Hypothesis

Step 5. State the conclusion of the hypothesis test.

A) There is sufficient evidence to support the claim that the mean pulse rate for smokers and non-smokers is different.

B) There is not sufficient evidence to support the claim that the mean pulse rate for smokers and non-smokers is different.

Answer 1

1)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0

2)

sample #1   ------->   smoker          
mean of sample 1,    x̅1=   76          
population std dev of sample 1,   σ1 =    9          
size of sample 1,    n1=   75          
                  
sample #2   --------->   non smoker          
mean of sample 2,    x̅2=   72          
population std dev of sample 2,   σ2 =    10          
size of sample 2,    n2=   73          
                  
difference in sample means = x̅1 - x̅2 =    76   -   72   =   4
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    1.5652          
                  
Z-statistic = ((x̅1 - x̅2)-µd)/SE =    4   /   1.5652   =   2.56

3)

p-value =        0.0106   [excel formula =2*NORMSDIST(z)]  

4)

Desison:   p-value>α=0.01 , Do not reject null hypothesis  

5)

B) There is not sufficient evidence to support the claim that the mean pulse rate for smokers and non-smokers is different.